Please find attached the images of triangle ΔABC after the dilation transformations with the following scale factors;
The coordinates of the triangle obtained from a similar question posted online are;
(2, 0), (5, 1), and (5, 0)
The center of dilation is (2, 0)
First part
The scale factor of dilation = 2
Given that the center of dilation is the point (2, 0) on the preimage, we have;
The coordinates of the image are;
(2, 0), (2 ×(5 - 2) + 2, (2 × (1 - 0)), (2 × (5 - 2) + 2, 0)
Which gives;
The coordinates of the vertices of the image are; (2, 0), (8, 2), (8, 0)
Please find the drawing of the image of the dilation of triangle ΔABC with a scale factor of 2 attached.
Second [part;
The scale factor = 3
Center of dilation = (2, 0)
The coordinates of the image are therefore;
(2, 0), (3 × (5 - 2) + 2, (3 × (1 - 0)), (3 × (5 - 2) + 2, 0)
Which gives;
(2, 0), (11, 3), and (11, 0)
Third part;
The scale factor = 12
Center of dilation = (2, 0)
The coordinates of the image are;
(2, 0), (12 × (5 - 2), 12 × (1 - 0)), (12 × (5 - 2), 0)
Which gives;
(2, 0), (36, 12), (36, 0)
Fourth part
Center of dilation = (2, 0)
Scale factor of dilation = s
The coordinates of the image are;
A(2, 0), C(s × (5 - 2) + 2), s × (1 - 0)), B(s × (5 - 2) + 2, 0)
Which gives;
Fifth part
The slope of the line is m, which is equal to the slope of the side [tex]\mathbf{\overline{AC}}[/tex], of ΔABC, which is given as follows;
[tex]m = \mathbf{\dfrac{1 - 0}{5 - 2}} = \dfrac{1}{3} [/tex]
The equation of the line in point and slope form is therefore;
[tex]y =\mathbf{ \dfrac{1}{3} \times (x - 2)}[/tex]
Which gives;
3·y = x - 2
Learn more about dilation transformation here:
https://brainly.com/question/12561082
